The 'progress' practice in PRINCE2 should be used to monitor and control the performance of the project against its plans and the project's overall direction. This includes predicting whether the benefits will exceed the costs, which is crucial for evaluating the project's ongoing viability and justifying the continuation of the project based on its forecasted value to the organization.References: (PRINCE2 7 Foundation Handbook, AXELOS)

The Plans theme in PRINCE2 estimates the cost of delivering the project. This theme involves the preparation and maintenance of the necessary schedules and budgets to control the project, including outlining how, when, and by whom the project's products will be delivered and at what cost.References:
PRINCE2 7 Foundation handbook and documents.

In the context of PRINCE2, the integrated elements include the principles, themes, processes, and tailoring PRINCE2 to the project environment. 'The products' are not listed as one of these integrated elements.
Instead, they are outputs or deliverables that result from applying the PRINCE2 methodology to project management. References: PRINCE2 Foundation manual, PRINCE2 official resources

The 'managing product delivery' process in PRINCE2 ensures that the planned products meet their quality criteria (ensuring products are fit for purpose) and that these products are delivered within the agreed tolerances (ensuring delivery within time, cost, quality, scope, risk, and benefit tolerances). References:
PRINCE2 Foundation Handbook, Managing Product Delivery section.

The purpose of the 'Quality' practice in PRINCE2 is to ensure that the project's products meet the documented expectations of the user or stakeholders. This involves defining quality requirements and standards for the project and its products and setting out the necessary activities to achieve these standards, thereby ensuring that the project delivers outputs that are fit for use.References: (PRINCE2 7 Foundation Handbook, AXELOS)